Researching the Value of Mathematics-Enhanced Linked Data

Mathematical operations are critical to managing data in Architecture, Engineering, and Construction (AEC). This is evident in the engineering standards that ensure the engineering practices, designs, and products are consistent and of high quality. These standards combine (1) textual descriptions and (2) mathematical information such as formulas and conditions. As organizations in the AEC sector strive for greater efficiency and collaboration, they increasingly use semantic information technologies, including Linked Data. These allow users to share and access data in a structured and machine-readable format.

Currently, semantic information works well for textual descriptions and is already used in standards such as IMBOR. However, expressing and using mathematics in Linked Data is less developed. Our innovation department is at the forefront of this field, i.e., Mathematics enhanced Linked Data, working on solutions that meet the needs of our clients. In this article, we delve into the research our intern Ani Mkheidze conducted in the field of Linked Data and mathematical operations. This research aimed to create a machine-readable format that reduces ambiguity in specifications (engineering standards), uses Linked Data to calculate and validate mathematical expressions, and makes it easier to share and understand mathematical information.

A mathematical expression, which we often encounter in engineering standards, is made of elements arranged in a specific way according to rules. The most common elements are numbers, variables, and operations. The research focuses on decomposing these expressions, which means breaking down complex equations into smaller and simpler parts. It involves separating the variables and clearly defining the operators and symbols used. For example, in the simple equation a + b, the variables (a & b) are separated, and the operator is +. The meaning of the operator (In this case, the +-sign) is established by linking them to a concrete definition that machines can understand, which is called an ontology. This way, new operations can always be added.

As part of our research, we created two models to solve the challenge of making it easier to share and understand mathematical information for software. The first model uses existing technology (SPARQL) to turn a mathematical equation into a format that computers and humans can read. The second model decomposes the equation and embeds it in Linked Data.  Both models do not require the user to write complicated expressions; an intuitive format exists for both. It is sufficient to provide the input data and the expressions, and the computer does the rest.

This research can potentially revolutionize how mathematical data is managed in the AEC sector, improving efficiency and collaboration between organizations.  Both models have successfully achieved the goal of calculating and validating expressions, enabling clients to integrate mathematics into software and standardize the process. The second model aimed to decompose expressions, reducing ambiguity and facilitating swift and clear sharing of mathematical information. If you want to learn more about our research, including detailed evaluations and case studies, contact Sander Stolk, Sebastiaan Hoeboer, or Ani Mkheidze.